Infrared small target detection (IRSTD) remains challenging due to the scarcity of useful target cues and the presence of severe background clutter. Most current methods rely on conventional feature learning and local interaction modeling, where features are represented in Euclidean space. However, such designs may still be limited in describing the subtle differences of weak targets and the contextual relations between targets and backgrounds. To address these limitations, we propose LoHGNet, an IRSTD network that integrates Lorentz geometric encoding with high-order relation learning. By introducing Lorentz manifold based feature learning, LoHGNet offers a different feature representation from conventional IRSTD methods and provides new discriminative cues for IRSTD. Specifically, a Lorentz encoding branch is constructed with the Geometric Attention Guided Lorentz Residual Convolution Module (GA-LRCM) to perform feature modeling under hyperbolic geometric constraints and enhance the hierarchical geometric representation capability of weak targets. Subsequently, the hyperbolic features are mapped into the Euclidean tangent space through logarithmic mapping, and a High-Order Relation Learning Module (HORL) is designed to model the high-order contextual dependencies between targets and backgrounds via hypergraph construction, thereby improving target discrimination in complex backgrounds. Experimental results on three datasets demonstrate that the proposed LoHGNet achieves competitive performance in both detection accuracy and adaptability to complex scenes. The code will be available at https://github.com/Kingwin97.